在無母數迴歸分析中，區域線性估計量同時具有較簡潔的漸進偏誤和較小的漸進變異數；然而，Seifert與Gasser(1996) 指出在有限樣本下，當資料稀疏或取樣點彼此很靠近時，區域線性估計量的條件變異數並沒有上界，估計出來的曲線因而崎嶇不平；為了改善這個問題，Seifert與Gasser(1996)結合了區域線性平滑法和脊迴歸的概念，建構出區域線性脊迴歸估計量。

本篇論文使用Seifert與Gasser (1996)的區域線性脊迴歸方法來估計同時具有多重線性迴歸式與無母數迴歸函數的半參數迴歸(semiparametric regression)模型，並利用交叉驗證法(cross validation)來選取最佳帶寬(bandwidth)和脊迴歸參數(ridge parameter)。根據模擬結果，當區域線性估計量和區域脊迴歸估計量均各自經由交叉驗證法選取其最適參數時，後者的無母數迴歸函數之估計式有明顯較小的樣本期望積分方差(sample mean integrated square error)並且其多重線性迴歸之參數估計式具有明顯較小的均方差(mean square error)。

In nonparametric regression analysis, local linear estimator (LLE) enjoys both smaller asymptotic bias and smaller asymptotic variance. However, Seifert and Gasser (1996) pointed out that in finite sample situations, when the design points are sparse or when design points are close to each other, LLE has unbounded conditional variance. The curve that estimated from the LLE has rough appearance accordingly; In order to improve this problem, Seifert and Gasser (1996) combines the local linear smoothing method and ridge regression to construct the local linear ridge regression estimator (LLRRE).

This thesis use local linear ridge regression method of Seifert and Gasser (1996) to improve the estimation of semiparametric regression which comprises both parametric and nonparametric regression component. A cross-validation method is used to select the optimal bandwidth and ridge regression parameters. According to the simulation results, when LLE and LLRRE both use their respective cross validated parameters, the LLRRE’s nonparametric regression function estimates have significantly smaller sample mean integrated square error than that of the LLE’s. And the latter method’s coefficient estimates of parametric regression component have significantly smaller mean square errors than that of the former’s.

目錄

第一章 緒 論	1
第一節 無母數迴歸分析簡介	1
第二節 半參數部分線性模型	4
第三節 區域線性估計量	5
第四節 有限樣本下的區域線性估計量	10
第五節 區域線性脊迴歸估計量	12
第二章 區域脊迴歸估計量與估計方法	15
第一節 估計方法	15
第二節 半參數部分線性模型與區域線性脊迴歸估計量	20
第三章 模擬研究	22
第一節 模擬設定及步驟	22
第二節 模擬結果	25
第四章 結論	33
第一節 研究結果	33
第二節 未來研究方向	34
參考文獻	35

表目錄

表 1：9
表 2：26
表 3：26
表 4：27
表 5：27
表 6：28
表 7：28
表 8：29
表 9：29
表 10：30
表 11：30
表 12：31
表 13：31


圖目錄

圖 1: 使用無母數方法，以收集到的資料直接估計函數	3
圖 2： 區域線性估計量在取樣點稀少或彼此靠近時，會產生估計效果不佳的情形	11

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